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Why is Australia mostly desert?

I'm working on the map for the world my DnD group is going to be playing in, and half of the continent they're starting on is similar to Australia in the way that it is mostly desert with some places that are pleasant. Here's a link to the country they're starting out in:

Because it's on the Tropic of Capricorn. The worst deserts are on this line and the Tropic of Cancer. Sure there are exceptions like the Gobi and the US southwest but these areas are the way they are because of low precipitation while the ones on the tropic lines are the way that they are because of the angle to the sun making them hotter. At least, this is what I remember from school...I'm sure someone will pop up in a bit with a wiki link. If you want this place to be a desert and it's not on a tropic line then put a wall of mountains in the west that kind of wraps around a bit to the north and south. Otherwise it will get a lot of rain from storms.

If the radiance of a thousand suns was to burst at once into the sky, that would be like the splendor of the Mighty One...I am become Death, the Shatterer of worlds.
-J. Robert Oppenheimer (father of the atom bomb) alluding to The Bhagavad Gita (Chapter 11, Verse 32)

I think Ascension is right about the tropics, except for one point: it's not because of the sun baking things (although that's what makes it a HOT desert), but it's still because of rainfall... Basically, because of the Coriolis Effect, wind patterns are driving moisture to and away from certain places. In the case of the Tropics, wind patterns are driving moisture away from those lines and toward either the Equatorial region (where we see a lot of hot, steamy rainforests) or toward the Temperate regions above and below the Tropics.

(1) Significantly greater evaporation than rainfall. Here in the Mojave desert where I live, we get about 5 inches a year of rainfall, but have about 300 inches a year of evaporation. Oftentimes what rainfall we get occurs over the span of a few hours, making for heavy flooding.

Things that make for greater evaporation than rainfall:

(a) being under the descending leg of a Hadley cell (see Hadley Circulation in your friendly neighborhood search engine). These areas fall roughly around 35 degrees north and south latitude here on the home planet. Just about where Australia sits in the south (and the Sahara in the north).

(b) being downwind of mountains. Mountains force air masses up, which makes them colder, colder air masses can hold less water so it drops as precipitation on the mountains. As the air comes down the backside of those mountains it warms again and the relative humidity drops to much lower than it was when it started up the mountains. In the case of the northern hemisphere deserts will be to the east of mountains due to Coriolis forces (forces due to the rotation of the spherical earth); in the southern hemisphere they will be on the west sides of mountains. In Australia, there is a lovely coastal range on the eastern edge of the continent with grassland grading to desert downwind of it.

(c) being far away from sources of moisture such as oceans. Rainfall happens. The more it happens the drier the air gets. If it happens long enough you don't get no rain no more and it's very dry. For example, the Gobi desert is very far downind from the nearest ocean. It's also a bit behind the Himalayas, but it's more a distance thing than rain shadow. Much of Australia is relatively far from oceans.

(d) being behind a cold offshort current. As the moist air masses pass over the current they get much colder, triggering the formation of fog and rain. This moisture is then unavailable for watering the desert areas. The Namib desert in Africa and the Atacama desert in South America have this condition (as well as being under a Hadley drop leg and having a rain shadow in the case of the Atacama).

And that's why Australia is mostly a desert except for the eastern mountain ranges that claw moisture out of the air, the northern reaches which are under a raising edge of a Hadley cell (rising edge=wet, falling edge=dry), and various relatively coastal areas.

In the case of the northern hemisphere deserts will be to the east of mountains due to Coriolis forces (forces due to the rotation of the spherical earth); in the southern hemisphere they will be on the west sides of mountains. In Australia, there is a lovely coastal range on the eastern edge of the continent with grassland grading to desert downwind of it.

Afraid you made a little mistake here. There is no difference between northern and southern hemispheres as far as the prevailing wind directions (and hence, direction of deserts relative to mountain ranges) goes.

It is in the equatorial region (roughly between the Tropics) that wind blows from east to west, potentially causing desertification to the west from mountains. When you get far enough from this region (either to the north or south) the winds will generally blow from west to east, and now the deserts will tend to be to the east from mountains. See the attached diagram for a visual explanation.